Mass Spectrum of Mesons via the WKB Approximation Method

Abstract

<jats:p>In this paper, we demonstrated that the multiple turning point problems within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method can be reduced to two turning point one for a nonsymmetric potential function by using an appropriate Pekeris-type approximation scheme. We solved the Schrödinger equation with the Killingbeck potential plus an inversely quadratic potential (KPIQP) function. The special cases of the modeled potential are discussed. We obtained the energy eigenvalues and the mass spectra of the heavy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>Q</mml:mi><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:math> and heavy-light <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>Q</mml:mi><mml:mover accent="true"><mml:mi>q</mml:mi><mml:mo stretchy="true">¯</mml:mo></mml:mover></mml:mrow></mml:mfenced></mml:math> mesons systems. The results in this present work are in good agreement with the results obtained by other analytical methods and available experimental data in the literature.</jats:p>

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

“…From this equation, we can get the energy spectrum as follows: We would like to note that the N-dimensional radial Schrödinger equation for the same potential is solved in [32], which should be the same as our result for N = 3 at zero temperature. Similar work with the Wentzel-Kramers-Brillouin approximation method has been studied at T = 0 temperature in [43]. At T = 0, the zero temperature limit of equation ( 38) reads as follows:…”

Analytical Solutions of the Schrödinger Equation with Class of Yukawa Potential for a Quarkonium System Via Series Expansion Method

“…We calculate mass spectra of charmonium and bottomonium for states from 1S to 1F, by using Eq. (34). The free parameters of Eq.…”

“…Al-Oun et al [33] examine heavy quarkonia ( ̅ , and ̅ ) characteristics in the general framework of a non-relativistic potential model consisting of a Coulomb plus quadratic potential. Furthermore, Omugbe et al [34] solved the SE with Killingbeck potential plus an inversely quadratic potential model. They obtained the energy eigenvalues and the mass spectra of the heavy and heavy-light meson systems.…”

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

“…In simulating the interaction potentials for these systems, confining-type potentials are generally used. The holding potential is the so-called Cornell potential with two terms, one of which is responsible for the Coulomb interaction of the quarks and the other corresponds to a confining term [7].…”